On pairwise compatibility graphs: a survey

Abstract

A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two nonnegative real numbers dmin and dmax such that each leaf u of T is a node of V and there is an edge (u, v) ∈ E if and only if dmin ≤ dT (u, v) ≤ dmax, where dT (u, v) is the sum of weights of the edges on the unique path from u to v in T. In this article, we survey the state of the art concerning this class of graphs and some of its subclasses